Where the [] will really be boxes and the | and -- marks will be solid lines.

So, I have 4 quadrants with boxes in each seperated by lines. I planned to make each quadrant its own JPanel holding JTextFields (the boxes need to accept text input), but the dividing lines part concerns me.

I know that I can use 2D to draw the lines by overriding paintComponent(), but how can I then position the panels to on top of the drawing?

Put each quadrant into a JPanel and set each JPanel's border to javax.swing.border.LineBorder. If the lines are two thick, try only setting two quadrants' borders (upper right, lower left). Warning: I am not a graphic designer!